how to solve DAE with bvp probelems?

hi everyone,

i have study maple for many days .now i have two questions about DAE with bvp probelem . maple 11 doesn't seem to solve the problems.the two problems are similar.

the question one is :

k1'(t)= -1              (1)      

k1(t)-2*a(t)*k2(t)=0       (2)

a(t)=v'(t)                 (3 )    

j(t)=a'(t)                (4)              

m-a^2(t)-g^2(t)=0          (5)       

g(t)*k2(t)=0               (6)

n+k2(t1)(m^2-g^2(t1))=0     (7)

the boundary is:v(0)=0    v(t1)=p(constant )    a(0)=0  a(t1)=0

where,  k1(t),k2(t),a(t),g(t),j(t),v(t) is fucntion of "t" ,t  range :0-t1 ,t1 is unkown ,m,n, p are known constant .

the question two  is :

x1’(t)=x2(t)       x1(t0)=x0                

x2’ (t)=u(t)          x2(t0)=v0       t0 ,tf ,x0,v0 ,v1  are kown constant 

k1’(t)=0            k1(tf)= -1      

k2’(t)=-k1(t)         x2(tf)=v1          

z(t)*k3(t)=0            

k2(t)=k3(t)[2*u(t)-u1-u2]             

z(t)*z(t)=[u(t)-u2]*[u1-u(t)]           u2<=u(t)<=u1    u1, u2 are kown constant 

where,  k1(t),k2(t),k3(t),z(t),u(t),x1(t),x2(t) is fucntion of "t" ,t  range :t0-t1 , t0 ,tf ,x0,v0 ,v1 ,u1, u2  are known constant 。

i have study many days but fail to solve ,can you give some help to solve them with numeric method?

contact me :meimeila123@sina.com    thank you !

any help or comment i will bi appreciated!

Please show us what you have tried so far

You will get more responses if you can show what you have tried in Maple, and more details about what specifically you have problems with.  Try posting your Maple worksheet to show others where the problem arises.

Robert Israel's picture

DAE

In the first example, from equation (6) either g(t) or k2(t) is 0.  If k2(t) = 0, then (2) says k1(t) = 0.  But this can't happen on any interval, because of equation (1).  So it must be g(t) = 0.  I'll leave the rest to you.

lots of thanks to Robert

lots of thanks to Robert Israel  !

 

 

the first example is a model derived from question two  set up on my own  . from Robert Israel's  analysis  i kow   the conditions a(0)=0  and a(t1)=0  are  wrong . the question two is an example from  textbook , the last three equations are nonlinear which are only  solved using numeric method.

 

 

aims to solve question two.

the first question is a model which i set up on my own derived from question two .the conditons   a(0)=0  a(t1)=0  are something wrong ,i am sorry about that .now aims to solve question two.

Robert Israel's picture

DAE

It looks to me like the DAE solver in dsolve can only do initial value problems, not boundary value problems.

As for Question 2, I think a similar hint to the one I gave for Question 1 should help.

k1(t) = -1, so k2(t) is nonzero except maybe at one point, so the same is true of k3(t),
so z(t) = 0 ...

 By the way, please don't ask the same question multiple times.

Comment viewing options

Select your preferred way to display the comments and click "Save settings" to activate your changes.
}